The glib answer to most questions about enhancing the Northeaster Dory's reserve flotation is "Southwester Dory."
Seriously, the Northeaster Dory is basically a bone-standard round-sided dory right out of the history books. None of those had ANY flotation aside from their woodiness, and by that standard the Northeaster Dory is practically a lifeboat. Certainly for casual usage the under-seat foam is ample and on at least two occasions we've been able to self-rescue our demo model following a capsize in deep water.
Compared to racing dinghies with a lot of decking and sealed tanks, a swamped Northeaster Dory can hold a lot of water. Were I to set out on any lengthy unsupported trip, I'd stow my gear in dry-bags and lash the bags low in the hull.
Besides being cold and wet, you have two major concerns in the aftermath of a swamping: the quantity of water to be evacuated, and the loss of stability resulting from the water swilling around inside the boat.
If the latter is your primary concern, putting your flotation up high is the best strategy. I've seen this done in Northeaster Dories; here's an example:

Between the foam beneath the thwarts and the flotation arrayed around the perimeter of the hull, this boat would be as stable as a floating dock if swamped. It would sit low, however, as the flotation up high won't do any floating until there's a lot of water aboard! You'd have a heap-load of bailing to do but at least you'd have a stable platform for it.
Placing the flotation down low displaces water that's come aboard, and starts working immediately. Buoyancy down low doesn't do as much for flooded stability, but you're going to have a whole lot less flooding to begin with, so this is the option I would choose. And in fact the Northeaster Dories that have featured in various stormy WaterTribe events were outfitted this way. (Click to embiggen.)

I would use a bunch of these carbon eyestraps, epoxied to the sides and bottom of the hull, to take the lashings for my dry-bags.

With the dry-bags distributed as shown in the drawing, the boat will float high and stable following a mishap. And as the saying goes, the best pump in the world is a scared sailor with a bucket. Just don't forget your bucket.